# Variability of volatility estimates from daily returns

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**Investment Performance Guy** has a post “Periodicity of risk statistcs (and other measures)” in which it is wondered how valid volatility estimates are from a month of daily returns.

Here is a quick look. Figure 1 shows the variability (and a 95% confidence interval) of volatility estimates for the S&P 500 index in January 2011. Figure 2 is for the first quarter and Figure 3 is for the first half. All of these are with daily data.

Figure 1: Volatility and bootstrap distribution for January 2011 volatility of the S&P 500.

Figure 2: Volatility and bootstrap distribution for Q1 of 2011 volatility of the S&P 500.

Figure 3: Volatility and bootstrap distribution for H1 of 2011 volatility of the S&P 500.

## Appendix R

The bootstrapping is done like:

`for(i in 1:1e4) spxvolQ1.boot[i] <- sd(spxret11Q1[sample(62,62, replace=TRUE)])`

The plots are something like:

`plot(density(spxvolM1.boot)*100*sqrt(252))`

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